Information on Result #1700480
Linear OOA(2174, 865, F2, 8, 30) (dual of [(865, 8), 6746, 31]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2174, 865, F2, 2, 30) (dual of [(865, 2), 1556, 31]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2174, 1039, F2, 2, 30) (dual of [(1039, 2), 1904, 31]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2172, 1038, F2, 2, 30) (dual of [(1038, 2), 1904, 31]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2172, 2076, F2, 30) (dual of [2076, 1904, 31]-code), using
- strength reduction [i] based on linear OA(2172, 2076, F2, 31) (dual of [2076, 1904, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(26) [i] based on
- linear OA(2166, 2048, F2, 31) (dual of [2048, 1882, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2144, 2048, F2, 27) (dual of [2048, 1904, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(26, 28, F2, 3) (dual of [28, 22, 4]-code or 28-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to Ce(30) ⊂ Ce(26) [i] based on
- strength reduction [i] based on linear OA(2172, 2076, F2, 31) (dual of [2076, 1904, 32]-code), using
- OOA 2-folding [i] based on linear OA(2172, 2076, F2, 30) (dual of [2076, 1904, 31]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2172, 1038, F2, 2, 30) (dual of [(1038, 2), 1904, 31]-NRT-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(2174, 432, F2, 40, 30) (dual of [(432, 40), 17106, 31]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |